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The recursive relation of the data distribution a(n) = a ( n - 1 ) x n - ( n - 1 ).

A sequence of values is defined by a mathematical equation termed as a recursive relation, also known as recursive relation. It derives current value(s) through specified initial value(s) and previous value dependent rule(s). In essence, it generates numeric sequences.

Note that every individual unit can be derived by multiplying the preceding one with a rising integer, and subsequently subtracting a descending integer:

1 x 1 - 0 = 1

1 x 2 - 1 = 1

1 x 3 - 2 = 5

5 x 4 - 3 = 17

17 x  5 - 4 = 71

71 x 6 - 5 = 247

We can deduce the relation of a(n) = a ( n - 1 ) x n - ( n - 1 ).

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The surface area of the prism is 112 in²

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of a prism is expressed as;

SA = 2B +pH

where h is the height and B is the base area and p is the perimeter of the base

The perimeter of the base = 2(l+b)

= 2(3+4) = 2×7 =14 in

The area of the base = l× b

= 4× 3 = 12 in²

height = 7

Therefore the surface area = 2 × 12 + 14 × 7

= 14+98

= 112 in²

therefore the surface area of the prism is 112 in²

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The three consecutive even integers are 6, 8, and 10, which satisfy the Pythagorean Theorem.

We have,

The Pythagorean Theorem in a right-angled triangle,

a² + b² = c²

To find three consecutive even integers that satisfy this theorem, we can start by assuming that one of the even integers is x.

Then, the next two consecutive even integers would be x+2 and x+4.

We can then use the Pythagorean Theorem to set up an equation and solve for x:

x² + (x+2)² = (x+4)²

Expanding and simplifying:

x² + x² + 4x + 4 = x² + 8x + 16

Simplifying further:

x² - 4x - 12 = 0

Now we can use the quadratic formula to solve for x:

x = [4 ± √(4² - 4(1)(-12))] / (2 x 1)

x = [4 ± √64] / 2

x = [4 ± 8] / 2

x = 6 or x = -2

Since we are looking for three consecutive even integers, we can discard the negative solution and choose x = 6.

This gives us the three consecutive even integers: 6, 8, and 10, which satisfy the Pythagorean Theorem:

6² + 8 = 10²

36 + 64 = 100

100 = 100

Thus,

The three consecutive even integers are 6, 8, and 10, which satisfy the Pythagorean Theorem.

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The complete question.

Find three consecutive even integers that satisfy the Pythagorean Theorem.

Answer: herefore, the average cost of the items Roy bought is $14.07.

Step-by-step explanation:

To find the average cost of the items Roy bought, we need to add up the total cost of all his purchases and divide by the total number of purchases.

Strategy:

1. Add up the cost of all Roy's purchases.

2. Count the number of purchases.

3. Divide the total cost by the number of purchases to find the average cost.

Explanation:

We will use this strategy because it is a straightforward way to find the average cost of multiple items. We will add up all the costs and divide by the number of purchases to get the average cost.

Calculations:

Total cost = (4 x $3.55) + $10.76 + $15.35 + $55.27 + $16.98

Total cost = $14.20 + $10.76 + $15.35 + $55.27 + $16.98

Total cost = $112.56

Number of purchases = 4 (coffee) + 2 (lunch) + 1 (groceries) + 1 (hardware store)

Number of purchases = 8

Average cost = Total cost / Number of purchases

Average cost = $112.56 / 8

Average cost = $14.07

Therefore, the average cost of the items Roy bought is $14.07.

This is a word problem, and the cost of one house in rubles is 1200, as the five sisters shared their father's inheritance equally.

If the three oldest sisters each paid 800 rubles, then they collectively paid 2400 rubles (800 rubles x 3 sisters) to the two younger sisters

Each of the the two younger sisters will have a total of 1200 rubles (2400 rubles/2 younger sisters), as they divided the money among themselves.

In conclusion, since the five sisters shared their father's inheritance equally, then 1200 rubles is the cost of one house, which solves the word problem

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Answer:

Arc length = (147/360) x (2π x 7)

Arc length = (0.40833) x (2 x 3.14159 x 7)

Arc length = 0.40833 x 43.9823

Arc length = 17.9955

Answer:

C -1

Step-by-step explanation:

in such a case the simplest way is to simply try the 4 numbers and see :

x² - 3x - 4 = |x + 3| - 2

x² - 3x - 2 = |x + 3|

A x = -4

(-4)² - 3×-4 - 2 = |-4 + 3|

16 + 12 - 2 = 1

26 = 1

wrong.

B x = -3

(-3)² - 3×-3 - 2 = |-3 + 3|

9 + 9 - 2 = 0

16 = 0

wrong.

C x = -1

(-1)² - 3×-1 - 2 = |-1 + 3|

1 + 3 - 2 = 2

2 = 2

correct.

D x = 4

4² - 3×4 - 2 = |4 + 3|

16 - 12 - 2 = 7

2 = 7

wrong.

The slope of f(x) is smaller than the slope of g(x).

For a linear function that passes through two points (x₁, y₁) and (x₂, y₂) the slope is given by the formula:

a = (y₂ - y₁)/(x₂ - x₁)

Then the slope of g(x) is:

a = (3 - 0)/(0 + 2) = 3/2

And for f(x) the slope is 4/5, then we can see that:

3/2 > 4/5

Thus the slope of g(x) is larger.

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Answer:

x^3 - 6x^2 + 12x - 8 = 0

Step-by-step explanation:

Let the roots of the equation x^3 - 8x + 3 = 0 be a, b, and c. Then, we know that the squares of the roots are a^2, b^2, and c^2.

By Vieta's formulas, we know that the sum of the roots of x^3 - 8x + 3 = 0 is 0, since there is no x^2 term:

a + b + c = 0

We also know that the product of the roots is 3/1 = 3:

abc = 3

Using the fact that the squares of the roots are a^2, b^2, and c^2, we can write:

a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + ac + bc)

Since a + b + c = 0, this simplifies to:

a^2 + b^2 + c^2 = -2(ab + ac + bc)

Now, let's try to find a cubic equation with roots a^2, b^2, and c^2. We can start with:

(x - a^2)(x - b^2)(x - c^2) = 0

Expanding the left side, we get:

x^3 - (a^2 + b^2 + c^2)x^2 + (a^2b^2 + b^2c^2 + c^2a^2)x - a^2b^2c^2 = 0

Using the identity we found earlier for a^2 + b^2 + c^2, we can simplify this to:

x^3 + 2(ab + ac + bc)x - 3a^2b^2c^2 = 0

Now, we can substitute in the values we know for ab, ac, and bc:

ab = (a + b + c)(ab + ac + bc) - (a^2b + ab^2 + c^2a)

ac = (a + b + c)(ab + ac + bc) - (a^2c + ac^2 + b^2a)

bc = (a + b + c)(ab + ac + bc) - (b^2c + bc^2 + a^2b)

Plugging in these values and simplifying, we get:

x^3 - 6x^2 + 12x - 8 = 0

Therefore, the cubic equation we're looking for is:

x^3 - 6x^2 + 12x - 8 = 0

And the roots of this equation are the squares of the roots of x^3 - 8x + 3 = 0.

The simplified expression is -7.1y - 7.8x + 14.8.

The given expression is 2.6y + 14.8 - 7.8x - 9.7y. To combine like terms, we first identify the terms that have the same variable with the same exponent. In this case, we have two terms with y, and they both have the exponent 1. So, we can combine these terms together by adding their coefficients, which are 2.6 and -9.7.

2.6y - 9.7y can be simplified as (2.6 - 9.7)y, which is equal to -7.1y. Therefore, the expression can be written as:

-7.1y - 7.8x + 14.8

We cannot combine any other terms in this expression since they do not have the same variable or exponent.

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The two sets of possible dimensions for the rectangular plot of land are:

11 m x 22 m

8 m x 28 m

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be A

Now , the length of the rectangle be L

Let the width of the rectangle be W

Let's assume that the length of the rectangular plot of land is L meters and the width is W meters. Since Jamal has only 44 meters of fencing available, the perimeter of the enclosure will be 44 meters:

Perimeter = 2L + W = 44

W = 44 - 2L

The area of the rectangular plot of land is given as 192 square meters

Area = L x W = L x (44 - 2L) = 192

2L² - 44L + 192 = 0

Solving for L using the quadratic formula, we get:

L = (44 ± √(44² - 4 x 2 x 192)) / (2 x 2)

L = (44 ± √(1600)) / 4

L = (44 ± 40) / 4

So, the possible values of L are 11 and 8

If L = 11, then W = 44 - 2L = 22, and the dimensions of the rectangular plot of land are 11 m x 22 m

If L = 8, then W = 44 - 2L = 28, and the dimensions of the rectangular plot of land are 8 m x 28 m

Hence , the two sets of possible dimensions for the rectangular plot of land are 11 m x 22 m and 8 m x 28 m

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Answer:

a = 48

b = 28

Step-by-step explanation:

b = 0.5 × 56

b = 28

52 = 0.5 × (56 + a)

104 = 56 + a

a = 48

Answer:

The sum of the interior angle measures of a regular hexagon is 720°.

Step-by-step explanation:

To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:

Sum of interior angles = (n - 2) × 180°

In the case of a hexagon, n = 6. So, we can plug this value into the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:

Sum of interior angles of hexagon = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

The absolute value inequality that has the solution set x ≤ –9 or x ≥ –5 is

|x + 7| ≤ 2

We have,

To write an absolute value inequality with a solution set x ≤ –9 or x ≥ –5, we first need to find the midpoint of the two given values:

Midpoint of –9 and –5

= (-9 + (-5)) / 2

= -7

We can now use the midpoint and one of the given values to write the absolute value inequality.

Since the solution set includes both values, we need to use the form

|x – b | ≤ c.

We can choose to use either value, let's use x ≤ –9:

|x – (-7)| ≤ |-9 – (-7)|

|x + 7| ≤ 2

Therefore,

The absolute value inequality that has the solution set x ≤ –9 or x ≥ –5 is

|x + 7| ≤ 2

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Yes, repeating two simple arithmetic operations will eventually transform every positive integer into 1.

From the question, we have the following parameters that can be used in our computation:

f(n) = n/2 if n%2 = 0

f(n) = 3n + 1 if n%2 = 1

The above definition means that

f(n) = n/2 if n is even

f(n) = 3n + 1 if n is odd

To check if repeating operations would transform to 1, we can set n = 10

and then evaluate the function values

So, we have

f(10) = 10/2 = 5

f(5) = 3(5) + 1 = 16

f(16) = 16/2 = 8

f(8) = 8/2 = 4

f(4) = 4/2 = 2

f(2) = 2/2 = 1

See that the end result of the operations is 1

Hence, repeating two operations will transform every positive integer into 1

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Answer:

d

Step-by-step explanation:

The first term is   'a'

  then for the second term    a r

      third  term =    a r^(n-1)

         etc  

The inches of water could Rafael have added is less than 3/8 inches

Given that

So, the inequality expression is

Initial water level - The decreased amount + Amount of water added by Rafael < The actual water level

Represent the Amount of water added by Rafael with x

So, we have

11 1/2 - 7/8 + x < 11

So, we have

92 - 7 + 8x < 88

When the like terms are evaluated, we have

8x < 88 + 7 - 92

Evaluate

8x <3

This gives

x < 3/8

Hence, the amount added by Rafael is less than 3/8 inches

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Answer:3

Step-by-step explanation:

The 80% confidence interval for the average water usage of 249 families is (15.42, 16.18) gallons.

To construct an 80% confidence interval for the average water usage of 249 families, we can use the following formula:

CI = X ± t(α/2, df) * (s/√n)

where X is the sample mean (15.8 gallons), t(α/2, df) is the critical t-value from the t-distribution table at the desired confidence level and degrees of freedom (247 in this case), s is the population standard deviation (1.7 gallons), and n is the sample size (249).

At an 80% confidence level and 247 degrees of freedom, the critical t-value is approximately 1.296.

Plugging in the values, we get:

CI = 15.8 ± 1.296 * (1.7/√249)

CI = 15.8 ± 0.38

Therefore, the 80% confidence interval for the average water usage of 249 families is (15.42, 16.18) gallons.

This means that we are 80% confident that the true average water usage of the population lies within this interval.

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The solution is the area of triangle ABC is 9.56 square units .

Given:

The objective is to find the area of triangle ABC

Explanation:

The general formula to find the area of a triangle is,

A = 1/2 *b*h

To find the area of triangle ABC:

The height of the triangle DC can be calculated using the Pythagorean theorem of triangle ADC.

DC  = √ 9 - 6.25

      =1.65

On plugging the given values in equation

Thus, the height of triangle ABC is 2.5

So the base of the triangle CB = 6 + 1.65 = 7.65.

Now, substitute the obtained values in equation

area = 1/2 * 7.65 * 2.5

        = 9.56

Hence, the area of triangle ABC is 9.56 square units .

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According to the given function.

There were approximately 24.9 million international Netflix subscriptions in the year 2012.

There were approximately 167.7 million international Netflix subscriptions in the year 2020,

We have,

a.

Since the function N(x) gives the number of international Netflix subscriptions x years after 2012, to find the number of Netflix subscriptions in the year 2012,

We need to set x = 0.

So,

N(0) = 24.9(1.736)^0

       = 24.9 million

b.

To estimate the number of Netflix subscriptions in the year 2020, we need to set x = 8 (since 2020 is 8 years after 2012).

N(8) = 24.9(1.736)^8

       =  167.7 million

Thus,

According to the given function.

There were approximately 24.9 million international Netflix subscriptions in the year 2012.

There were approximately 167.7 million international Netflix subscriptions in the year 2020,

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Answer:

The height of the desk is 8 cubic inches.

Hope this helps!

Step-by-step explanation:

The formula for the volume of a rectangular prism is Width × Length × Height or Base × Height.

Because the Base is already given ( 400 in² ), that means the height of the desk can be found by dividing 3200 by 400.

3200 ÷ 400 = 8

The height of the desk will be 8 cubic inches.

The probability of getting exactly 9 of them major in STEM is 0.139 or 13.9%.

The probability of getting at most 11 of them major in STEM is approximately 0.898 or 89.8%.

The probability of getting at least 11 of them major in STEM is approximately 0.318 or 31.8%.

a. Exactly 9 of them major in STEM.

In this case, the probability of success (a student majoring in STEM) is 0.27, and the number of trials is 35. The probability of exactly 9 students majoring in STEM is then given by the formula:

P(X = 9) = (35 choose 9) x (0.27)⁹ x (0.73)²⁶

where (35 choose 9) is the number of ways to choose 9 students out of 35, and (0.27)⁹ x (0.73)²⁶ is the probability of 9 successes and 26 failures. Evaluating this expression gives a probability of approximately 0.139 or 13.9%.

b. At most 11 of them major in STEM.

To calculate the probability that at most 11 students out of 35 major in STEM, we can use the cumulative binomial probability distribution. This distribution calculates the probability of at most X successes, where X is any number from 0 to the total number of trials.

The probability of at most 11 students majoring in STEM can be calculated as follows:

P(X <= 11) = P(X = 0) + P(X = 1) + ... + P(X = 11) = 0.898 or 89.8%.

c. At least 11 of them major in STEM.

The probability of less than 11 students majoring in STEM can be calculated using the cumulative binomial probability distribution, as in part (b). Specifically:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)

Subtracting this probability from 1 gives the probability of at least 11 students majoring in STEM:

P(X >= 11) = 1 - P(X < 11) = 31.8%

Again, we can use the binomial distribution formula from part (a), or a binomial probability calculator or statistical software package to calculate this probability.

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Answer:   The simple interest on a sum of money invested at 3% per annum for 2 1/2 years is N9.225, and the principal is N3,000.

Step-by-step explanation:

We can use the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Given that the interest is N123, the interest rate is 3% per annum, and the time is 2 1/2 years, we can plug these values into the formula and solve for the principal:

123 = P * 0.03 * 2.5

Simplifying, we get:

123 = 0.075P

P = 123 / 0.075

P ≈ 1,640

Therefore, the principal is approximately N1,640.

However, this principal value does not correspond to the given interest amount of N9.225. To obtain the correct principal, we need to use the correct interest amount:

We can convert the time of 2 1/2 years to 5/2 years, and use the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Given that the interest is N9.225, the interest rate is 3% per annum, and the time is 5/2 years, we can plug these values into the formula and solve for the principal:

9.225 = P * 0.03 * 5/2

Simplifying, we get:

9.225 = 0.0375P

P = 9.225 / 0.0375

P = 246

Therefore, the principal is N246.

The selling price of the antique through an online auction website is $680.

Given that,

Kyle sold an antique through an online auction website.

The website host charges Kyle $15, plus 2.5% of the final selling price of the antique.

After selling the antique, Kyle had to pay the website host $32.

Let x be the selling price of the antique.

We get an equation,

15 + (2.5% × x) = 32

15 + 0.025x = 32

0.025x = 17

x = $680

Hence the selling price is $680.

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Answer:

The amount of money the painter earns, in dollars, depends on the number of rooms he paints.

For each room painted, the painter charges $25. Therefore, the amount of money earned, y, is given by the equation:

y = 25x + 100

where x is the number of rooms painted and 100 is the cost of supplies.

To graph this equation, we can plot a point on the y-axis where x=0 (the fixed cost of supplies) at (0, 100), and then use the slope of 25 to find additional points. For example, when x=1, y=125; when x=2, y=150; and so on.

With this information, we can eliminate options (b) and (d) because they both show negative slopes, which would mean the painter loses money as he paints more rooms.

Option (c) shows a positive slope, but the line goes through the point (0,100) and (4,200), which means the painter earns $200 after painting 4 rooms, but this contradicts the given information that the painter charges $25 per room. Therefore, option (c) is also incorrect.

Option (a) correctly shows the slope of 25 and goes through the point (0, 100), and the line reaches the x-axis when x=4, indicating that the painter earns $0 after painting 4 rooms. This matches the given information that the painter charges $25 per room. Therefore, the correct answer is option (a).

Therefore, the graph that shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints is:

a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 0

Answer:

The correct answer is a C. coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200.

The painter pays $100 for supplies, so he will only earn money for the rooms he paints after he has recouped that cost. The first room he paints will earn him $25, the second will earn him $50, and so on. After he has painted 4 rooms, he will have earned $200.

The graph of this relationship would be a line that starts at the point (0, 100) and goes up to the point (4, 200).

Step-by-step explanation:

Answer:

The equation of the line is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

From the given equation, we can see that the y-intercept is 19. This means that the line passes through the point (0, 19).

Therefore, the coordinates of the y-intercept are (0, 19).

The y-intercept of the equation y=6x+19 is the value of y when x equals 0, which is at the point (0,19).

Therefore, in the equation y=6x+19, the y-intercept is at the point (0, 19). Hence, the coordinates of the y-intercept are (0,19).

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Answer: 1:4

Step-by-step explanation:

In order to do this, we have to know that the octagon has an area which is four times less than the other area. Because of this, it shuld be 1:4